85 more than a square of a number is the same as the sum of the square of the quantity that is 17 less than the number. What is the number?

Let N be the number

85 + N^2 = ( N - 17)^2 simplify

85 + N^2 = N^2 - 34N + 289 subtract N^2 from both sides

85 = -34N + 289 subtract 289 from both sides

85 - 289 = -34N

-204 = -34N divide both sides by -34

6 = N

Amione, you already answered that question yourself, why are you asking that question again?

Cphill's solution is wrong, because he got from

85+N^{2}=N^{2}-34*N+289 to

85= 34*N+289

the answer is N=6, not N=-6

Slight sign error...now corrected...!!!